You are trying to measure the height of your house but only have a surveyor tool that measures angles and you know your sidewalk is exactly 25 feet from the base of your home. From the sidewalk, you find that the measure of the angle of elevation to the top of your house is 58 degrees. How tall is your house to the nearest foot? Please show all work in order to get full credit.
To find the height of the house, we can use the tangent function.
Let's consider the right triangle formed by the house, the sidewalk, and the line of sight to the top of the house.
In this triangle, the angle opposite to the base of the house is 58 degrees (angle of elevation).
We know that the base of the house is 25 feet (distance from the sidewalk).
Using the tangent function, we have:
tan(58 degrees) = Height of the house / 25 feet
Solving for the height of the house:
Height of the house = tan(58 degrees) * 25 feet
Using a calculator:
Height of the house = 1.376381920471173 * 25 feet
Height of the house ≈ 34.41 feet
Therefore, the height of the house is approximately 34.41 feet when rounded to the nearest foot.